To a Riemannian three-manifold equipped with a torsion spin^c structure one can naturally associate a b_1-dimensional family of twisted Dirac operators. Even though the topological properties of such family are explicitly described by the Atiyah-Singer index theorem in terms of the triple cup product, its geometric features are much less understood. In this talk, I will discuss how monopole Floer homology can be used to provide information on the latter for manifolds with a large spectral gap on coexact 1-forms, with a focus on concrete examples.

日時 : （Talk 2）2024年１月11日（木）　10時～11時
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締切日：2024年１月４日（木）17時厳守